quaternion.h

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// -*- Mode: C++; tab-width: 2; -*-
// vi: set ts=2:

#ifndef BALL_MATHS_QUATERNION_H
#define BALL_MATHS_QUATERNION_H

#ifndef BALL_MATHS_MATRIX44_H
# include <BALL/MATHS/matrix44.h>
#endif

#ifndef BALL_MATHS_VECTOR3_H
# include <BALL/MATHS/vector3.h>
#endif

#include <boost/math/quaternion.hpp>
#include <iostream>

namespace BALL
{

  template <typename T>
  class TQuaternion
    : public boost::math::quaternion<T> //{/*...*/};
  {
    public:

    BALL_CREATE(TQuaternion<T>)

    

    TQuaternion();

    TQuaternion(const TQuaternion& q);

    TQuaternion(const boost::math::quaternion<T>& q);

    TQuaternion(const T& w, const T& i, const T& j, const T& k);

    TQuaternion(const TVector3<T>& axis, const T& angle);

    ~TQuaternion();

    void clear();



    void set(const TQuaternion& q);

    void set(const boost::math::quaternion<T>& q);

    BALL_DEPRECATED
    void set(const TVector3<T>& axis, const T& angle);

    void set(const T& w, const T& i, const T& j, const T& k);

    TQuaternion& operator = (const TQuaternion& q);

    TQuaternion& operator = (const boost::math::quaternion<T>& q);

    void setIdentity();

    TQuaternion<T>& normalize();

    void swap(TQuaternion& q);

    void fromAxisAngle(const TVector3<T>& axis, const T& angle);

    void fromEulerAngles(const T& yaw, const T& pitch, const T& roll);

    void toAxisAngle(TVector3<T>& axis, T& angle);

    void toEulerAngles(T& yaw, T& pitch, T& roll);
    //void toEA(T& yaw, T& pitch, T& roll);

    void get(TQuaternion& q) const;

    T getAngle() const;

    TVector3<T> getAxis();

    TMatrix4x4<T>& getRotationMatrix(TMatrix4x4<T>& m) const;

    TQuaternion getInverse() const;

    TQuaternion getConjugate() const;


    T& w();

    const T& w() const;

    T& i();

    const T& i() const;

    T& j();

    const T& j() const;

    T& k();

    const T& k() const;




    void dump(std::ostream& s = std::cout, Size depth = 0) const;

  };

  template <typename T>
  TQuaternion<T>::TQuaternion()
    : boost::math::quaternion<T>()
  {
    this->setIdentity();
  }

  template <typename T>
  TQuaternion<T>::TQuaternion(const TQuaternion& q)
    : boost::math::quaternion<T>(q)
  {
  }

  template <typename T>
  TQuaternion<T>::TQuaternion(const boost::math::quaternion<T>& q)
    : boost::math::quaternion<T>(q)
  {
  }

  template <typename T>
  TQuaternion<T>::TQuaternion(const T& w, const T& i, const T& j, const T& k)
    : boost::math::quaternion<T>(w, i, j, k)
  {
  }

  template <typename T>
  TQuaternion<T>::TQuaternion(const TVector3<T>& axis, const T& angle)
    : boost::math::quaternion<T>()
  {
    fromAxisAngle(axis, angle);
  }

  template <typename T>
  TQuaternion<T>::~TQuaternion()
  {
  }

  template <typename T>
  void TQuaternion<T>::clear()
  {
    this->setIdentity();
  }

  template <typename T>
  void TQuaternion<T>::set(const TQuaternion<T>& q)
  {
    boost::math::quaternion<T>::operator= (q);
  }

  template <typename T>
  void TQuaternion<T>::set(const boost::math::quaternion<T>& q)
  {
    boost::math::quaternion<T>::operator= (q);
  }

  template <typename T>
  BALL_INLINE
  void TQuaternion<T>::set(const TVector3<T>& axis, const T& angle)
  {
    fromAxisAngle(axis, angle);
  }

  template <typename T>
  BALL_INLINE
  void TQuaternion<T>::set(const T& w, const T& i, const T& j, const T& k)
  {
    this->a = w;
    this->b = i;
    this->c = j;
    this->d = k;

  }

  template <typename T>
  BALL_INLINE
  TQuaternion<T>& TQuaternion<T>::operator = (const boost::math::quaternion<T>& q)
  {
    set(q);
    return *this;
  }

  template <typename T>
  BALL_INLINE
  TQuaternion<T>& TQuaternion<T>::operator = (const TQuaternion<T>& q)
  {
    set(q);
    return *this;
  }

  template <typename T>
  BALL_INLINE
  void TQuaternion<T>::setIdentity()
  {
    this->a = (T)1;
    this->b = this->c = this->d = (T)0;
  }

  template <typename T>
  BALL_INLINE
  TQuaternion<T>& TQuaternion<T>::normalize()
  {
    T length = boost::math::norm(*this);

    if (!(Maths::isEqual(length, (T)0)))
    {
      this->a /= length;
      this->b /= length;
      this->c /= length;
      this->d /= length;
    }
    return *this;
  }

  template <typename T>
  void TQuaternion<T>::swap(TQuaternion<T>& q)
  {
    T tmp = q.a;
    q.a = this->a;
    this->a = tmp;

    tmp = q.b;
    q.b = this->b;
    this->b = tmp;

    tmp = q.c;
    q.c = this->c;
    this->c = tmp;

    tmp = q.d;
    q.d = this->d;
    this->d = tmp;
  }

  template <typename T>
  void TQuaternion<T>::fromAxisAngle(const TVector3<T>& axis, const T& angle)
  {
    T length = axis.getLength();

    if (Maths::isEqual(length, (T)0))
    {
      this->b = this->c = this->d = (T)0;
      this->a = (T)1;
    }
    else
    {
      T omega = (T) (angle * 0.5);
      T sin_omega = (T)::sin(omega);

      this->a = (T)::cos(omega);
      this->b = axis.x * sin_omega / length;
      this->c = axis.y * sin_omega / length;
      this->d = axis.z * sin_omega / length;
    }
  }

  template <typename T>
  void TQuaternion<T>::fromEulerAngles(const T& yaw, const T& pitch, const T& roll)
  {
    T half_yaw = yaw / 2.0;
    T half_pitch = pitch / 2.0;
    T half_roll = roll / 2.0;

    T cosYaw = cos(half_yaw);
    T sinYaw = sin(half_yaw);

    T cosPitch = cos(half_pitch);
    T sinPitch = sin(half_pitch);

    T cosRoll = cos(half_roll);
    T sinRoll = sin(half_roll);


    this->a = cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw;
    this->b = sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw;
    this->c = cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw;
    this->d = cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw;

  }

  template <typename T>
  void TQuaternion<T>::toAxisAngle(TVector3<T>& axis, T& angle)
  {
    T length = sqrt(this->b*this->b + this->c*this->c + this->d*this->d);

    if (Maths::isEqual(length, (T)0))
    {
      axis.x = axis.y = angle= (T)0;
      axis.y = (T)1;
    }
    else
    {
      angle = 2 * (T)::acos(this->a);
      axis.x = this->b / length;
      axis.y = this->c / length;
      axis.z = this->d / length;
    }
  }


  template <typename T>
  void TQuaternion<T>::toEulerAngles(T& yaw, T& pitch, T& roll)
  {
    TMatrix4x4<T> matrix;
    getRotationMatrix(matrix);
    T sinYaw, cosYaw, sinPitch, cosPitch, sinRoll, cosRoll;

    sinPitch = -matrix(2,0);
    cosPitch = sqrt(1 - sinPitch*sinPitch);

    if ( fabs(cosPitch) > Constants::EPSILON)
    {
      sinRoll = matrix(2,1) / cosPitch;
      cosRoll = matrix(2,2) / cosPitch;
      sinYaw = matrix(1,0) / cosPitch;
      cosYaw = matrix(0,0) / cosPitch;
    }
    else
    {
      sinRoll = -matrix(1,2);
      cosRoll = matrix(1,1);
      sinYaw = 0;
      cosYaw = 1;
    }

    /* yaw */
    yaw = atan2(sinYaw, cosYaw);

    /* pitch */
    pitch = atan2(sinPitch, cosPitch);

    /* roll */
    roll = atan2(sinRoll, cosRoll);

  }

  template <typename T>
  BALL_INLINE
  void TQuaternion<T>::get(TQuaternion<T>& q) const
  {
    q.set(*this);
  }

  template <typename T>
  T TQuaternion<T>::getAngle() const
  {
    T length = sqrt(this->b*this->b + this->c*this->c + this->d*this->d);
    if (Maths::isEqual(length, (T)0))
    {
      return (T)(0);
    }
    else
    {
      return (T)(2 * (T)::acos(this->a));
    }
  }

  template <typename T>
  TVector3<T> TQuaternion<T>::getAxis()
  {
    T length = sqrt(this->b*this->b + this->c*this->c + this->d*this->d);
    if (Maths::isEqual(length, (T)0))
    {
      return TVector3<T>((T)0,(T)0,(T)1);
    }
    else
    {
      return TVector3<T>(this->b/length, this->c/length, this->d/length);
    }
  }

  template <typename T>
  TMatrix4x4<T>& TQuaternion<T>::getRotationMatrix(TMatrix4x4<T>& m) const
  {
    T s = 2.0 / boost::math::norm(*this);
    m.set
      (
        (T)(1.0 - s * (this->c * this->c + this->d * this->d)),
        (T)(s * (this->b * this->c - this->d * this->a)),
        (T)(s * (this->d * this->b + this->c * this->a)),
        (T)0,

        (T)(s * (this->b * this->c + this->d * this->a)),
        (T)(1.0 - s * (this->d * this->d + this->b * this->b)),
        (T)(s * (this->c * this->d - this->b * this->a)),
        (T)0,

        (T)(s * (this->d * this->b - this->c * this->a)),
        (T)(s * (this->c * this->d + this->b * this->a)),
        (T)(1.0 - s * (this->c * this->c + this->b * this->b)),
        (T)0,

        (T)0,
        (T)0,
        (T)0,
        (T)1
      );

    return m;
  }

  template <typename T>
  BALL_INLINE
  TQuaternion<T> TQuaternion<T>::getInverse() const
  {

    return conj(*this) / boost::math::norm(*this);
  }

  template <typename T>
  BALL_INLINE
  TQuaternion<T> TQuaternion<T>::getConjugate() const
  {
    return conj(*this);
  }

  template <typename T>
  const T& TQuaternion<T>::w() const
  {
    return this->a;
  }

  template <typename T>
  T& TQuaternion<T>::w()
  {
    return this->a;
  }

  template <typename T>
  const T& TQuaternion<T>::i() const
  {
    return this->b;
  }

  template <typename T>
  T& TQuaternion<T>::i()
  {
    return this->b;
  }

  template <typename T>
  const T& TQuaternion<T>::j() const
  {
    return this->c;
  }

  template <typename T>
  T& TQuaternion<T>::j()
  {
    return this->c;
  }

  template <typename T>
  const T& TQuaternion<T>::k() const
  {
    return this->d;
  }

  template <typename T>
  T& TQuaternion<T>::k()
  {
    return this->d;
  }

  template <typename T>
  std::istream& operator >>(std::istream& s, TQuaternion<T>& q)
    
  {
    char c;
    s >> c >> q.w() >> c >> q.i() >> c >> q.j() >> c >>q.k() >> c;
    return s;
  }

  template <typename T>
  std::ostream& operator << (std::ostream& s, const TQuaternion<T>& q)
    
  {
    s << '(' << q.w() << ',' << q.i() << ','
             << q.j() << ',' << q.k() << ')';

    return s;
  }

  template <typename T>
  void TQuaternion<T>::dump(std::ostream& s, Size depth) const
  {
    BALL_DUMP_STREAM_PREFIX(s);

    BALL_DUMP_HEADER(s, this, this);

    BALL_DUMP_DEPTH(s, depth);
    s << "    w: " << this->w() << std::endl;

    BALL_DUMP_DEPTH(s, depth);
    s << "    i: " << this->i() << std::endl;

    BALL_DUMP_DEPTH(s, depth);
    s << "    j: " << this->j() << std::endl;

    BALL_DUMP_DEPTH(s, depth);
    s << "    k: " << this->k() << std::endl;

    BALL_DUMP_STREAM_SUFFIX(s);
  }



  typedef TQuaternion<float> Quaternion;

} // namespace BALL

#endif // BALL_MATHS_QUATERNION_H